Here we are, still stuck. A fifth of Britain's 11-year-olds, children not born when Blair was elected, can't read well enough to cope with school. Statistically, they're set for failure now. Only 5% will catch up enough to get five worthwhile GCSEs. Ministers confess themselves puzzled by the continued failure of those at the bottom to learn. Whatever we're doing in schools to give all children a chance, it isn't working. So what can we try next?

This is the holy grail of centre-left politics. How do you prevent poor children from being fatally handicapped by their backgrounds? Across the ocean, President Obama thinks he's found the answer. He plans to reproduce it in 20 US cities – and it comes from a unique project in Harlem.

The Harlem Children's Zone (HCZ) is a fiercely ambitious programme to change the achievements and expectations of every one of the 10,000 children living in 97 blocks of one of the most devastated communities in America. An eight-year-old boy from Harlem has a 33% chance of ending up in prison. Three-quarters of Harlem schoolchildren can't pass the grade exams for their age. A third of students drop out of high school. Unemployment is double the average. The hundreds of millions in community support and educational initiatives tried in Harlem over the past decades have effectively achieved almost nothing. Some lives have been turned around, but the grim backdrop of most people's existence has remained stubbornly unchanged.

That realisation drove the HCZ founder, Geoffrey Canada, to revolutionise the way he worked. Canada had been a community organiser in Harlem since 1990, and he was fed up with rescuing one drug addict, or criminal, or failing schoolchild, only to watch another dozen slip away. A radical change of approach was needed, and he thought two bold ideas could form the basis for it.

The first was the concept of the tipping point. In Harlem, poverty was so great, and crime and drugs so prevalent, that only the exceptionally lucky or driven child could avoid joining in. Canada wanted to raise the expectations of the whole community simultaneously, so that going to college or avoiding teenage pregnancy would become normal behaviour. Focusing on a minority of talented children wasn't enough. But if 60% of the peer group were ambitious, hardworking and supported by adult, all those antisocial pressures would alter too.

This wasn't just some utopian fantasy. Canada had a theory for how it could be done. All the latest research on the brain showed that much of a child's capacity to think and to learn was set in the first three years of life. Middle-class families were spending those years talking, singing and reading to their children. Poor children weren't getting any of that. They were arriving at school with an average of 25 hours of one-to-one reading behind them. Middle-class children had had 1,700 hours, and their vocabulary was twice as large. They had learned to argue and discuss, and had been introduced to conceptual thinking. Above all, the middle-class children arrived with confidence. They had been encouraged. By the age of three they had heard six times as many encouraging words as discouraging ones. Poor children had been reprimanded two and a half times more than they had been praised. Meanwhile, James Heckman, a Nobel prize-winning economist, showed that by the late teenage years, deprived children were very hard to help or teach new skills.

Canada's plan was simple, and staggering. Forget the dozens of small, uncoordinated interventions, many aimed at helping adults. If he could only change the way Harlem's children were raised, he could end the cycle of despair, and transform their future. He wanted to create a pipeline for achievement that would start before birth, with parenting classes that revolutionised adults' approach to their babies, and continued until after college. It would be a tight safety net, involving pre-kindergartens, academies, tutoring, dance and sport classes, food co-ops, social service, and help with housing and health. Every child in the zone would be offered support, and school admission would be done by lottery. It would engage the whole community in a project to transform the lives of the next generation. It was too late for Harlem's adults to expect radical change for themselves, but it could be done for their children.

On the strength of his vision, Canada raised millions of dollars – one-third from the government, two-thirds from philanthropists and charities. The total cost would by $5,000 per child per year.

Five years after Canada opened the first of his Promise academy schools, initially with kindergarten and sixth-grade (for 12-year-olds) classes, a Harvard University study has just evaluated what it calls "one of the most ambitious social-service experiments of our time". The schools' intake is random, and very deprived: 10% of the children live in homeless shelters or foster care. Yet Harvard concludes that even in a few short years, the combination of community transformation, high-quality teaching and parental support has been "enormously effective at raising the achievement level of the poorest minority children". Whereas the American pattern is for the black/white achievement gap to start wide and become a gulf, so that only 7% of black 14-year-olds pass their grade in maths, the Promise academies are reversing that. Some 97% of their eighth-graders are performing at or above grade level. The elementary school has closed the racial gap in language and in maths, and the pre-kindergarten children are outperforming their white counterparts.

The effects of the HCZ are, says Harvard, much greater than all other initiatives tried across the country – whether it's lowering class size, giving bonuses to teachers in tough schools, or running the classic early-childhood programmes like Head Start. Studying the HCZ offers "many opportunities to answer the important questions that have evaded social scientists for decades".

What the Harlem experiment tells us is that our own piecemeal approaches are never going to deliver real change for those at the bottom. The HCZ is starting where it matters, with the plasticity of babies' brains, and it's trying to recreate, in homes and in the community, what prosperous children already get – sustained care and concern over a lifetime. We, by contrast, keep trying little interventions – like Sure Start – where we engage with families for a couple of years and then retreat, hoping they've learned what they needed. It doesn't work. Without continuity, the effects don't last.

The other lesson of Harlem is that no change comes cheap. Quality is everything. The kindergartens have one teacher for every four children. In the academies half the teachers left – they were not suited to the job – at the end of the first year. Rolling this out to other poor neighbourhoods will cost America billions. But the potential prize is astonishing – the raising of many children's achievement beyond what we ever thought possible. Officially, British ministers like Liam Byrne and John Denham are said to be waiting to see what we can learn from Harlem. This is not a good time to be suggesting radical spending plans. But if we're not prepared to take ambitious action like this, we can't claim to be surprised that the poorest children just don't achieve.